An Information Hiding Scheme Based on Pixel- Value-Ordering Prediction-Error Expansion with Reversibility Ching-Chiuan Lin Department of Information Management Overseas Chinese University Taichung, Taiwan Shih-Chieh Chen Department of Information Management Overseas Chinese University Taichung, Taiwan Kuo Feng Hwang Department of Information Technology Overseas Chinese University Taichung, Taiwan Abstract This paper proposes a data hiding scheme based on pixel-value-ordering predication-error expansion. In a natural image, most neighboring pixels have similar pixel values, i.e. the difference between neighboring pixels is small. Based on the observation, we may predict a pixel s value according its neighboring pixels. The proposed scheme divides an image into non-overlapping blocks each of which consists of three pixels, pixels in a block are sorted in a descending order. Messages are embedded into two difference values, where one is between the largest medium pixels the other is between the smallest medium ones. In the embedding process, difference values equal to 0 or greater than 1 are unchanged or increased by 1, respectively, those equal to 1 are also unchanged or increased by 1 if the message bit to be embedded is equal to 0 or 1, respectively. Calculating the difference value, one may extract a message bit of 0 or 1 if it is equal to 1 or 2, respectively. Recovering pixels is done by decreasing those difference values by 1 if they are equal to or larger than 2. Experimental results demonstrate that the proposed scheme may provide much larger embedding capacity, comparing to existing study, a satisfied image quality. Keywords Reversible data hiding; Pixel-value-ordering; Prediction-error expansion I. INTRODUCTION Digital image is a digitized medium stored in an electronic file for presenting objects to people. If someone would like to know more about the image, a separated voice or text file is required, which is an inconvenient way. Alternatively, the owner of the image may type texts on the image for giving more information about the image to a viewer. This may damage or distort the image the amount of added texts is limited. In addition, distorting an important image, e.g. a medical image, is unaccepted, since a distorted medical image may result in an incorrect diagnosis. Data hiding is a way of imperceptibly embedding important information into a medium, which may provide a way for annotating or watermarking an image, or secret communication. An image with embedded information is called a stego-image. Usually, the stego-image is visually the same as its original image so that people may not perceive the embedded objects. When data are embedded into an image, the image may be distorted. In general, the more data we embed, the more the image would be distorted. Embedding capacity image distortion is a tradeoff. Therefore, a good data hiding scheme should be able to embed as many messages as possible distort the cover image as slightly as it could. How to embed a large amount of data into an image achieve a slightly distorted image is an important issue for data hiding applications. The issue is more important if we want the distorted image to be recoverable. A famous scheme for reversibly embedding messages into an image, based on difference expansion, was proposed by Tian [1] in 2003. Based on differences between neighboring pixels in an image are small, his scheme exps a difference value between two neighboring pixels by increasing or decreasing their pixel values. Specifically, if a difference value between pixels is calculated as, the difference is exped to, where if. Then, a message bit is embedded into the exped difference by setting, if is expable, i.e. are not over or under saturated. Later, for an expable difference, the embedded message may be extracted by calculating, are recovered by, where. Since we cannot guarantee that every difference is expable, a location map recording whether a difference is expable or not is required. Fortunately, most differences are expable the location map may be compressed in a satisfied compression ratio so that it consumes only a small part of embedding space. Later, a number of studies [2-5] inspired by Tian s scheme were proposed. In 2006, a novel reversible data hiding scheme, based on shifting pixel histogram, was proposed by Ni et al. [6]. They calculated the number of pixels with the same pixel value obtained a pixel histogram where the peak point was selected for embedding messages. Since most images contain few pixels with very small or large pixel values, the histogram on the right or left of peak point may be shifted one to the right or left side, respectively, so that there would be available space for embedding messages. A number of studies based on shifting histogram were proposed. References [7-10] improved Ni et al. s scheme by shifting difference histogram, instead of 1 P a g e
pixel histogram. Since difference between neighboring pixels usually is small, the peak point of difference histogram would be much higher than that of pixel histogram. Generally, these schemes have a higher embedding capacity comparing to those based on shifting pixel histogram. A group of studies [11-16] explored neighboring pixels in an image predicted a pixel value by its neighboring pixels. Then they adopted the histogram of predicted error for embedding messages. In general, the peak point of prediction error histogram is higher than difference histogram. Nevertheless, the embedding capacity of this kind of approach depends on its predictive method. This paper proposes a data hiding scheme based on pixelvalue-ordering predication-error expansion. In a natural image, most neighboring pixels have similar pixel values, i.e. the difference between neighboring pixels is small. Based on the observation, we may predict a pixel s value according its neighboring pixels. The proposed scheme divides an image into non-overlapping blocks each of which consists of three pixels, pixels in a block are sorted in a descending order. Messages are embedded into two difference values, where one is between the largest medium pixels the other is between the smallest medium ones. In the embedding process, difference values equal to 0 or greater than 1 are unchanged or increased by 1, respectively, difference values equal to 1 are also unchanged or increased by 1 if the message bit to be embedded is equal to 0 or 1, respectively. Calculating the difference value, one may extract a message bit of 0 or 1 if it is equal to 1 or 2, respectively. Recovering pixels is done by decreasing those difference values by 1 if they are equal to or larger than 2. Experimental results demonstrate that the proposed scheme may provide much larger embedding capacity, comparing to existing study, a satisfied image quality. The rest of this paper is organized as follows. Section II briefly reviews Li et al. s scheme [15]. The proposed scheme is introduced in Section III. Section IV demonstrates our experimental results compares the performance of the proposed scheme with that of Li et al. s. Finally, conclusions are given in Section V. II. RELATED WORK Li et al. [15] proposed a data hiding scheme based on pixelvalue-ordering predication-error expansion. First, their scheme divides an image into non-overlapping blocks each of which consists of four pixels as shown in Fig. 1(a). The four pixel values in a block are sorted in an ascending order as shown in Fig. 1(b) where denote the sorted pixels. Then calculate { where are the stego-pixel of the message bit to be embedded, respectively. In Fig. 1(c), the stego-pixel is (i.e. ) this block may not embed a message bit since. Finally, the stego-pixels would be. If (i.e. ), the embedding result would be unchanged, i.e.. In case of, the embedding result would be or if the message bit to be embedded is or, respectively. 20 25 22 23 (a) 20 22 23 25 (b) 20 22 23 26 Fig. 1. An embedding process example of Li et al. s scheme The recovery process is the reverse of its embedding process. If one would like to extract an embedded message bit from a stego-block recover a stego-pixel to its original pixel, he/she may calculate { (c) { { } The rationale of Li et al. s scheme is based on the concept of pixel values in a block are similar for a natural image. Namely, the difference of pixel values in a block is small they predicted a difference value (denoted by ) of one. If the difference is larger than one (i.e., they increased by one so that there would be an available space of for embedding a message bit into a block. Then if the message bit to be embedded is 0 or 1, is unchanged or set to 2, respectively. III. PROPOSED SCHEME The proposed scheme includes the embedding extraction processes. The former embeds secret messages into a cover image obtains a stego-image, the latter extracts the embedded secret messages from the stego-image completely recovers it to its original image. Most studies avoid the problem of saturated conditions (i.e. pixel value equal to 0 or 255 for a 2-gray-level image). It is worth mentioning that the proposed scheme also includes a solution for solving the 2 P a g e
problem of saturated conditions. The two processes are presented in the following, respectively. A. Embedding process This section shows the embedding process for a cover image I with n pixels. Let the secret message, with bits, to be embedded be a bit string, where { }. The embedding process is shown as follows. 1) For a gray-level image I, divide it into non-overlapping blocks each of which contains three neighboring pixels denoted by,,, respectively, where. 2) For each block, sort their pixel values in a descending order denoted by,,, where,,, are the largest, medium, smallest values, respectively, in block. 3) Embed by setting stego-pixel values of, respectively, as { The problem of recording saturated blocks with pixels modified is taken into account in step 3, it is recorded by the overhead information embedded in the blocks mentioned in step 4. Note that we would not encounter the problem of saturated blocks in step 4. B. Extraction process Whenever a decoder gets the setgo-image, he/she may follow the following process to extract the embedded message completely recover image to its original image I. In the process, the decoder could determine whether a saturated block needs to be recovered or not, from the extracted overhead information. The extraction process is presented as follows. 1) Divide setgo-image as it was divided by the encoder in the embedding process. 2) As in the embedding process, for each block, sort their pixel values,, in a descending order denoted by,,, where,, are the largest, medium, smallest stego-pixel values, respectively, in block. 3) For each block with, calculate extract { { (3) if or, where are the prediction errors of, respectively. Mark a block with or as overhead information. Let be the required overhead information for extracting the embedded messages, where is its length, { },. 4) Let be the sub-message embedded in step 3, where denotes concatenating. For each block with, embed by performing (1) (2). Overhead information would not be generated in this step since in this step. 5) Finally, the stego-image is obtained. In step 2, if the pixels in block are sorted in an ascending, the embedding process in steps 3 4 would still be workable. However, for simplicity, the embedding process selects the descending order. The proposed scheme applies the medium value in a block to predict its neighboring pixel values. The rationale is that, in a natural image, most image blocks are smooth. Thereby we may expect that pixel values of are similar to that of the prediction error would be small. This implies that we would obtain more embedding space for embedding a message than without prediction. { (4) where is a bit of mixed messages. Then perform { { Extract from those blocks with. Note that the bit order of is determined by the block index. Specifically, if is extracted from block, would be extracted from block where. 4) Given in step 3, recover stego-pixels extract message bits from those blocks with or. 5) According to the block index, rearrange the message bits extracted from blocks, in steps 3 4, with or to get the sub-message. Another submessage may be extracted from blocks, in step 3, with. Finally, is obtained the original cover image I is completely recovered. 3 P a g e
Block H/M 0 145 148 147 148 147 145 1 149 147 144 144 149 147 1 147 148 149 149 148 147 01 149 148 146 146 148 149 2 146 146 145 146 146 145 1 146 146 144 146 146 144 3 2 2 2 2 2 2 2 2 249 2 249 2 4 1 2 4 4 2 1 0 5 2 1 1 2 5 5 1 2 4 4 2 1 1 5 2 0 0 2 5 6 0 2 3 3 2 0 3 2 0 0 2 3 Fig. 2. An example of the proposed scheme (a) Lena (b) Baboon (c) Airplane Fig. 3. Test images (d) Pepper (e) Gold (f) Boat C. An example of the proposed scheme An example with 7 blocks is given in this section to illustrate the proposed scheme. The example image is a graylevel one with pixel values between 0 255. In the embedding process, the divided blocks are shown in Fig. 2, where column H/M denotes both overhead information message bits to be embedded. Pixel values in a block are sorted in a descending order the largest smallest pixel values in a block are marked by red blue color, respectively. Let the message to be embedded be. The first processed block is, in step 3, block 3 which embeds nothing, is embedded into block 4 by setting =1. Then is embedded into block 5. Block 6 is a saturated block its pixels is remained unchanged, in this step. For simplicity, assume the overhead information is. In step 4, is embedded into blocks 0 1, is embedded into blocks 1 2. Note that block 1 embeds two bits, one is from the second bit of the other is from the first bit of. After is embedded, the embedding process is completed. Moving to the extraction process, we divide setgo-image into non-overlapping blocks as it was divided by the encoder in the embedding process sort pixel values in a descending order for each block. First, in step 3, mixed messages of,, are extracted from blocks 0 4 by performing (3) (4) these blocks are recovered by performing (5) (6). Next, the overhead information is extracted from blocks 0 3, since in these blocks. For simplicity, assume that means that block 5 needs to be recovered. Then a bit of 1 is extracted from block 5, the block is recovered. After all messages are extracted 4 P a g e
(IJACSA) International Journal of Advanced Computer Science Applications, Lena 0 3 6 9 12 15 18 21 24 27 30 33 36 Baboon 0 2 4 6 8 10 12 14 16 18 (a) Lena (b) Baboon Airplane 0 5 10 15 20 25 30 35 40 45 Pepper 0 4 8 12 16 20 24 28 32 36 40 44 (c) Airplane (d)pepper Gold 0 3 6 9 12 15 18 21 24 27 30 33 36 39 Boat 0 3 6 9 12 15 18 21 24 27 30 33 36 (e) Gold Fig. 4. Comparing performance of the proposed scheme with Li et al. s scheme (f) Boat 5 P a g e
Maximun (IJACSA) International Journal of Advanced Computer Science Applications, Proposed Li et al. 40 30 20 10 0 Lena Baboon Airplane Pepper Gold Boat Images Fig. 5. Comparison of maximum embedding capacity stego-pixels are recovered, is obtained from blocks with or by rearranging the extracted bit string according to their block indexes. Similarly, is obtained from the above mixed messages but removing the last bit (i.e. the first bit of ). Finally, is extracted the cover image is completely recovered. From the above example, we observe that both stegoblocks 5 6 are saturated blocks. However, stego-block 5 needs to be recovered, in the extraction process, the block must be distinguished from stego-block 6 which was not changed in the embedding process. The problem about whether a saturated block needs to be recovered or not may be solved by the embedded overhead information. In step 3 in the extraction process, we first extract messages from stego-blocks with or, since these blocks would not be saturated ones. Then we decode overhead information from blocks with. As long as the overhead information was decoded, we can recognize which saturated blocks need to be recovered. Note that blocks with or embed user s messages, if any, instead of overhead information in step 3 in the embedding process. The example in the section has illustrated how the overhead information is embedded into extracted from a stego-image. IV. EXPERIMENTAL RESULTS To evaluate the performance of proposed scheme, we implemented the proposed scheme in Java on a personal computer embedded romly generated secret messages into cover images, as shown in Fig. 3, which were downloaded from [17]. All cover images are grayscale with 2 levels the dimension is. A test image may be divided into non-overlapping blocks. In the extreme condition, if a block embeds two bits, the embedding capacity of an image may be up to 17 bits. Each in a block may be modified no more than one. For a 2-gray-level image with n pixels, the image quality, or the similarity between a stego-image its cover image, is evaluated by peak signal to noise ratio (PSNR) calculated as as In the above equation, MSE is mean square error calculated where denote cover stego-pixel values, respectively. We also implemented Li et al. s scheme, on the same platform, to compare the performance of our scheme with their scheme s. An image applying the proposed scheme may obtain a larger number of blocks comparing to applying Li et al. s. Therefore, the image may provide a larger embedding capacity if it applies the proposed scheme. A smooth image (e.g. Airplane) may contain a larger number of smooth blocks comparing to a complex image (e.g. Baboon). Here a smooth block is an image block with similar pixel values, it may result in a smaller prediction error. The proposed scheme embeds a message bit into a block with prediction error equal to one which is a smaller prediction error. Since Baboon Airplane are smooth complex images, respectively, their prediction errors are usually larger smaller, respectively, than the other test images. Fig. 4 illustrates the comparison of performance between the proposed Li et al. s schemes in terms of image quality (PSNR) embedding capacity. The figure shows, in a low embedding capacity, the two schemes have similar performance. We can observe that the PSNR is higher than db for each test images in Fig. 4, the proposed scheme may provide image quality similar to Li et al. s scheme but a much higher embedding capacity than their scheme. In the worst condition, if is increased by one is decreased by one, we have 6 P a g e
. This means the proposed scheme may guarantee the image quality higher than 49.89 db for a 2-gray-level image. Even in this condition, the difference between a cover image its stego-image would not be detected by human eye. Fig. 5 shows the comparison of maximum embedding capacity between the proposed Li et al. s schemes. For the test images in Fig. 3, the embedding capacity of the proposed scheme is more than twice as high as Li et al. s. A reason is that we may embed, at most, two message bits into a block, whereas Li et al. s scheme may embed, also at most, only one message bit into a block. In addition, the proposed scheme could provide more blocks than Li et al. s. The proposed scheme may satisfy more applications requirement if they need a higher embedding capacity satisfied image quality. V. CONCLUSIONS We have introduced an information hiding scheme, with reversibility, based on pixel-value-ordering predictionerror expansion. The proposed scheme divides an image into non-overlapping blocks each of which contains three pixels sorts pixels in a block in a descending order. After embedding, the property of pixel-value-ordering in a block is invariant so that the image can be recovered. Comparing to Li et al. s scheme, the proposed scheme can achieve more blocks for embedding. In addition, a block may embed up to two message bits. Consequently, the proposed scheme can obtain a higher embedding capacity satisfied image quality. Experimental results show that the proposed scheme achieves an embedding capacity more than twice as high as Li et al. s scheme on the same level of image quality. The proposed scheme is a good cidate for reversible data-hiding applications which need a high embedding capacity low distortion. REFERENCES [1] J. Tian, Reversible data embedding using a difference expansion, IEEE Transactions on Circuits Systems for Video Technology, vol. 13, pp. 890 896, August 2003. [2] A. M. Alattar, Reversible watermarking using the difference expansion of a generalized integer transform, IEEE Transactions on Image Processing, vol. 13, pp. 1047 11, August 2004. [3] C. C. Chang T. C. Lu, A difference expansion oriented data hiding scheme for restoring the original host images, Journal of Systems Software, vol. 79, pp. 17 17, December 2006. [4] D. M. Thodi J. J. Rodríguez, Expansion embedding techniques for reversible watermarking, IEEE Transactions on Image Processing, vol. 16, pp. 1 730, March 2007. [5] O. M. Al-Qershi B. E. Khoo, High capacity data hiding schemes for medical images based on difference expansion, Journal of Systems Software, vol. 84, pp. 105 112, January 2011. [6] Z. Ni, Y. Q. Shi, N. Ansari, W. Su, Reversible data hiding, IEEE Transactions on Circuits Systems for Video Technology, vol. 16, pp. 3 3, March 2006. [7] C.-C. Lin N.-L. Hsueh, A lossless data hiding scheme based on three- pixel block differences, Pattern Recognition vol. 41, pp. 1415 1425, April 2008. [8] C.-F. Lee H.-L. Chen, Adjustable prediction-based reversible data hiding, Digital Signal Processing, vol. 22, pp. 941 953, December 2012. [9] W.-L. Tai, C.-M. Yeh, C.-C. Chang, Reversible data hiding based on histogram modification of pixel differences, IEEE Transactions on Circuits Systems for Video Technology, vol. 19, pp. 906 910, June 2009. [10] C.-C. Lin,W.-L. Tai, C.-C. Chang, Multilevel reversible data hiding based on histogram modification of difference images, Pattern Recognition, vol. 41, pp. 32 3591, December 2008. [11] P. Tsai, Y.-C. Hu, H.-L.Yeh, Reversible image hidings cheme using predictive coding histogram shifting, Signal Processing, vol. 89, pp. 1129 1143, June 2009. [12] V. Sachnev, H. J. Kim, J. Nam, S. Suresh, Y. Q. Shi, Reversible watermarking algorithm using sorting prediction, IEEE Transactions on Circuits Systems for Video Technology, vol. 19, pp. 989 999, July 2009. [13] W. Hong T.-S. Chen, A local variance-controlled reversible data hiding method using prediction histogram-shifting, Journal of Systems Software, vol. 83, pp. 2653 23, December 2010. [14] W. Hong, T.-S. Chen, Y.-P. Chang, C.-W. Shiu, A high capacity reversible data hiding scheme using orthogonal projection prediction error modification, Signal Processing, vol. 90, pp. 2911 2922, November, 2010. [15] X. Li, J. Li, B. Li, B. Yang, High-fidelity reversible data hiding scheme based on pixel-value-ordering prediction-error expansion, Signal Processing, vol. 93, pp. 198 205, January 2013. [16] B. Ou, X. Li, Y. Zhao, R. Ni, Reversible data hiding using invariant pixel-value-ordering prediction-error expansion, Signal Processing: Image Communication, in press. [17] http://sipi.usc.edu/database/ 7 P a g e